The divorce between Paramount and DreamWorks meant that rights issues stalled any further US Ring movies after The Ring Two. For a while there was talk of a Ring 3D, but that project has now morphed into something called **Rings, which is sounding like more of a reboot than a threequel. Whatever its direction, it at least now has a star. Relative newcomer Matilda Lutz has signed up for the ordeal.
Last we heard, F. Javier Gutiérrez (Before The Fall) was directing, and Akiva Goldsman was writing a new draft of the screenplay begun by David Loucka. Nothing is yet known about the storyline, but we can perhaps surmise that Lutz will be the recipient of a videotape (or perhaps some sort of updated media) that puts her on the receiving end of a haunting by well-dwelling *yūrie *ghoul Samara (the American version of Sadako). Word on the street is that Rings will maintain some sort of continuity with the previous two American films.
Interestingly, though it's probably irrelevant, Rings was also the title of the short film Jonathan Liebesman directed to accompany the American Ring Two in 2005.
The Ring cycle, of course, begins in 1991 with Koji Suzuki's novel, and comes to international attention with Hideo Nakata's terrifying Japanese adaptation in 1998. That was followed by sequel Rasen, but when that didn't do very well there was another, different Ring 2, followed by prequel Ring 0.
Meanwhile in the US, Gore Verbinski directed the remake The Ring in 2002, and Nakata himself directed The Ring Two in 2005, which was not a remake of the Japanese Ring 2, but borrowed a lot from Dark Water. Following this? More recently in Japan they've had Sadako 3D and Sadako 3D 2, which both follow Rasen, which everybody used to ignore. There's also a Korean remake and a Japanese TV version that predates the first film.
If you think all that's complicated you should check out The Grudge.
Back in American threequel land, Lutz is actually Italian, and significantly younger than past Ring protagonists. She's previously appeared in Giovanni Veronesi's The Fifth Wheel and Albert Kodagolian's Somewhere Beautiful, and currently has two other Italian films in post-production, so "up-and-coming" might seem a good description. Rings will be her American debut, but there's no reported start date yet.